A combination of fractal analysis and artificial neural network to forecast groundwater depth



A concern that researchers usually face in different applications of Artificial Neural Network (ANN) is determination of the size of effective domain in time series. In this paper, fractal analysis was used on groundwater depth time series to determine the size of effective domain in the series in an observation well in Union County, New Jersey, U.S. The variation method was applied to the sets considering different domains of 20, 40, 60, 80, 100, and 120 preceding days and the fractal dimension was determined. The fractal dimension remained constant (1.52) when the length of the domain decreased below 80 days. Data sets in different domains were fed to a Feed Forward Back Propagation ANN with one hidden layer and the the groundwater depths were forecasted. Root Mean Square Error (RMSE) and the correlation factor (R2) of estimated and observed groundwater depths for all domains were determined. In general, groundwater depth forecast improved, as evidenced by lower RMSEs and higher R2s, when the domain length increased from 20 to 120. However, 80 days was selected as the effective domain because the improvement was less than 1% beyond that. Forecasted groundwater depths utilizing measured daily data (set #1) and data averaged over the effective domain (set #2) were compared. It was postulated that the more accurate nature of the measured daily data was the reason for a better forecast with lower RMSE (0.1027 m compared to 0.255 m) in set #1. However, a major drawback was the size of the input data in this set which was 80 times the size of the input data in set #2; a factor that may increase the computational effort unpredictably. Hence, it was concluded that fractal analysis may be successfully utilized to lower the size of input data sets considerably, while maintaining the effective information in the data set.